CN113220023B - A high-precision real-time path planning method for unmanned aerial vehicles - Google Patents

Abstract

The invention relates to a high-precision real-time path planning method for unmanned aerial vehicles, and belongs to the field of precise control of unmanned aerial vehicles. The method includes the following steps: S1: establish a linear state differential equation of the UAV, and obtain the constraints of the UAV itself and the environment; S2: establish a kinematic error model of the UAV; S3: convert the solving problem into a linear equivalent Equation solving problem; S4: Set a number of different UAV path targets according to environmental constraints; S5: Use deep learning method to perform matrix decomposition to solve the control function parameters; S6: Determine whether the solved control parameters meet the constraints of the UAV itself condition. The method of the invention can greatly reduce the calculation amount, import multiple targets solved by the dynamic geometric method in real time, and use the deep learning method to obtain a high-precision control function, so as to realize the real-time high-precision path planning of the UAV.

Description

A high-precision real-time path planning method for unmanned aerial vehicles

technical field

The invention relates to a high-precision UAV real-time path planning method, belongs to the field of UAV precise control, and is especially suitable for UAV multi-target high-precision path planning scenarios.

Background technique

With the maturity of UAV control technology, UAVs have been widely used in military and civilian fields such as battlefield environment reconnaissance, ground target strike, power line patrol, and aerial photography. UAV path planning is particularly important in UAV applications. Commonly used path planning methods can be divided into geometric methods, heuristic search methods, potential field methods and so on. Among them, the geometric method first performs geometric modeling of the environment, and then selects a certain search algorithm to obtain a feasible solution according to a certain optimal strategy. However, when the task space changes, the task space needs to be re-traversed, and the amount of calculation is large, so it is not suitable for Dynamic trajectory planning; heuristic search methods include classical algorithms such as A* algorithm, particle swarm algorithm, genetic algorithm, etc. With the expansion of the search space, the computational complexity of such algorithms will explode, so real-time The typical method of potential field method is artificial potential field method, which has the advantages of reducing the amount of calculation and improving real-time performance, but it is easy to fall into local optimum. Some methods are only suitable for offline planning, but the external environmental factors are uncertain, and the UAV is limited by dynamic constraints, such as the maximum turning angle and detection radius, so it has great limitations in the application process.

Although the improvement or combination of the above can reduce the amount of calculation and improve the real-time performance, it also greatly sacrifices the control accuracy, and cannot complete the multi-objective dynamic path planning problem.

SUMMARY OF THE INVENTION

The invention provides a high-precision real-time path planning method for unmanned aerial vehicles, which attempts to transform the unmanned aerial vehicle path planning problem into a linear equation solving problem in an off-line manner, greatly reduces the amount of calculation, and imports the dynamic geometry method in real time to solve multiple problems. The target, and the deep learning method is used to obtain a high-precision control function to realize the high-precision path planning of the UAV.

To achieve the above object, the present invention provides the following technical solutions:

A high-precision UAV real-time path planning method, comprising the following steps:

S1: Establish the linear state differential equation of the UAV based on the principle of small disturbance linearization, and obtain the UAV's own constraints and environmental constraints;

S2: Use the interpolation method to establish the kinematic error model of the UAV;

S3: Convert the solving problem of the UAV kinematic error model into a linear equation solving problem equivalently;

S4: Set multiple different UAV path targets according to environmental constraints;

S5: Bring the path target of the UAV as a boundary condition into the linear equation of the UAV, set the control function type, and use the deep learning method to perform matrix decomposition to solve the control function parameters;

S6: Determine whether the solved control parameters satisfy the constraints of the UAV itself, if so, execute the control flight; if not, delete the solution, and repeat steps S5-S6 until no solution is satisfied, correct the unmanned aerial vehicle If there is still no solution and the upper limit of the calculation time is reached, an early warning of no solution of the path is performed.

Further, the linear state differential equation of the UAV described in step S1 is a constant coefficient differential equation, such as: x′(t)=dx(t)/dt=A x(t)+u(t), t∈[t ₀ , t _f ], where A is the n×n-dimensional UAV state matrix, which is determined according to the dynamic model of the UAV; u(t) is the n-dimensional control vector with respect to time; x( t) is the state vector of the n-dimensional UAV, n is a positive integer, usually the UAV speed, position and attitude angle.

其中，h_i＝t_i+1-t_i，τ＝(t-t_i)/h_i，α₀(τ)＝2τ³-3τ²+1，α₁(τ)＝τ³-τ²+τ，β₀(τ)＝-2τ³+3τ²，β₁(τ)＝τ³-τ²，τ∈[0，1]。Further, the interpolation method described in step S2 is the Hermit cubic spline interpolation method. In any time interval t∈[t _i , t _i+1 ], a constant coefficient differential equation described in step 1 can be obtained by the interpolation method in any dimension. symbolic expression for the approximate solution of the previous

Wherein, hi =t _{i +1} -t _i , τ=(tt _i )/ _hi , α ₀ (τ)=2τ ³ -3τ ² +1, α ₁ (τ)=τ ³ -τ ² +τ , β ₀ (τ)=−2τ ³ +3τ ² , β ₁ (τ)=τ ³ −τ ² , τ∈[0,1].

Furthermore, the interval of the Hermit cubic spline interpolation method is an interval of equal duration so as to greatly reduce the amount of calculation, and the specific number of divisions i can be adjusted according to the actual accuracy requirement.

进一步，对误差进行二次型建模得到无人机运动学误差模型

Further, the error of the UAV kinematics in step S2 in the segment t∈[t _i , t _i+1 ] is

Further, quadratic modeling of the error is carried out to obtain the kinematic error model of the UAV

Further, the step S3 is specifically:

代入Hermit三次样条插值方程，进一步，得到分段误差二次型

其中，y_i＝[x(t_i)，x′(t_i)，x(t_i+1)，x′(t_i+1)]^T，

b_i＝α₁′E-α₁h_iA，

d_i＝β′₁E-β₁h_iA，E为n×n维的单位矩阵；S301: For each segment

Substitute into the Hermit cubic spline interpolation equation, and further, obtain the quadratic form of piecewise error

where y _i =[x(t _i ), x'(t _i ), x(t _i+1 ), x'(t _i+1 )] ^T ,

b _i =α ₁ ′E-α ₁ h _i A,

d _i =β′ ₁ E-β ₁ h _i A, E is an n×n-dimensional identity matrix;

恒大于0，且当控制变量确定时为一个常数，因此从误差二次型中删除该项；S302: Due to

is always greater than 0, and is a constant when the control variable is determined, so this item is deleted from the error quadratic;

S303: Convert the UAV kinematic error model to obj=min(y ^T Fy-2By), where F is the (2n·i+2n)×(2n·i+2n) dimension corresponding to the superposition matrix of F _i , B is a vector of (2n·i+2n) dimension correspondingly superimposed by B _i , y=[x(t ₀ ), x′(t ₀ ), x(t ₁ ), x′(t ₁ ), . . . , x (t _f ), x′(t _f )] ^T is the superposition of (2n·i+2n) dimension y _i ; where x′(t _i ) is the derivative of x(t _i ) at time t _i with respect to time t ;

S304: In the case of full rank, there is a unique solution to obj=min(y ^T Fy-2By), and the solution is Fy=B.

Further, step S4 is specifically as follows: according to the environmental constraints, the path planning is carried out by the geometric method, the midpoint or state of the flight path is selected as the path target, and its value is set as the path y=[x(t ₀ ), x′( t ₀ ), x(t ₁ ), x′(t ₁ ), …, x(t _f ), x′(t _f )] multiple different UAV path target values in ^T , that is, the part in y parameters are known.

Further, the step S5 is specifically:

S501: Set the type of the undetermined control function u(t) with parameters according to requirements; usually, to reduce the amount of calculation and ensure the accuracy, one or two polynomial types with parameters about time t are selected.

求解

得到

(2)判断

对应元素距离步骤S4中设定的多个路径目标的数值y是否都符合设定的误差范围要求，如果符合则停止训练，输出控制函数，如果不符合，则继续训练直到符合为止。所述的深度学习技术通常采用神经网络。S502: Use deep learning to solve Fy=B, and train the parameters of the control function u(t); specifically: (1) Substitute randomly selected points within the interval as parameters of the control function into B to obtain

solve

get

(2) Judgment

Whether the numerical values y of the multiple path targets set in the corresponding element distance step S4 all meet the set error range requirements, if so, stop training and output the control function, if not, continue training until it meets. The deep learning techniques described generally employ neural networks.

Preferably, in steps S1-S3 of the present invention, the corresponding linear relationship matrix of the UAV can be obtained by offline calculation, and then, the path target point solved by the dynamic environment geometry method can be directly imported in the application in an online mode, The optimal path control parameters are directly solved.

Preferably, after the linear relationship matrix is obtained through steps S1-S3 of the method of the present invention, it can be directly used to calculate the high-precision path of the known control function, that is, given F and B, to solve y.

In particular, in order to improve the calculation accuracy, the number of path targets can be increased, or the step size h _i can be subdivided, but at the same time, the amount of calculation will be increased. However, when the same step size divides the time interval, the error of the method of the present invention is the smallest.

The beneficial effects of the present invention are as follows: the present invention provides a high-precision real-time path planning method for unmanned aerial vehicles, which converts the multi-objective path planning problem with the smallest unmanned aerial vehicle error into a linear equation solving problem, greatly reduces the amount of calculation, Importing multiple targets solved by dynamic geometric methods, and using deep learning methods to obtain high-precision control functions, realizes real-time high-precision path planning for UAVs.

Description of drawings

In order to make the purpose and technical solution of the present invention, the present invention provides the following drawings for description:

Fig. 1 is a flow chart of a real-time path planning method for a high-precision UAV;

FIG. 2 is a schematic diagram of superposition of F and B in Example 1 of the present invention.

Detailed ways

In order to make the objectives and technical solutions of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

Example 1: Take a UAV described in the paper "Simulation Analysis and Research of UAV Mathematical Model Based on Matlab" published by Rong Hui et al. as an example, it is now necessary to control the UAV to execute within t∈[0,10] seconds At the beginning, all state variables are 0. At a specific time t=5 seconds, the environmental constraints of the UAV are required to be the flight speed of V(5)=1m/s ² and the pitch angle of θ(5 )=0°, height H(5)=10m; the self-constraint condition is that the elevator deflection angle is not greater than 30°. The present invention provides "a high-precision real-time path planning method for unmanned aerial vehicles". In conjunction with Fig. 1, the method includes the following steps:

S1: Using the principle of linearization based on small disturbance, establish a linear state differential equation of UAV kinematics, and obtain state data at the initial moment of UAV.

According to the constant coefficient differential equation of longitudinal motion described in the paper, the form is as follows: x'(t)=dx(t)/dt=A·x(t)+u(t),

Among them, A=A _long is a 5×5-dimensional constant coefficient matrix, which is determined according to the dynamic model of the UAV; u(t)=B _long ·[δ _e , δ _T ] ^T is the control vector about time; x (t)=[V, α, q, θ, H] ^T is the state vector of the UAV, where V is the flight speed, α is the angle of attack, q is the pitch angular velocity, θ is the pitch angle, and H is the height.

S2: Use the interpolation method to establish the kinematic error model of the UAV. Specifically:

First, divide the time interval into 10 equal parts in units of 1 second, for any part h _i =1;

其中，τ＝t-t_i，α₀(τ)＝2τ³-3τ²+1，α₁(τ)＝τ³-τ²+τ，β₀(τ)＝-2τ³+3τ²，β₁(τ)＝τ³-τ²，τ∈[0，1]；Then, using the interpolation method of Hermit cubic spline interpolation method, in any time interval t∈[t _i , t _i+1 ], a constant coefficient differential equation described in step 1 can be obtained by interpolation method in any dimension. symbolic expressions for approximate solutions

Wherein, τ=tt _i , α ₀ (τ)=2τ ³ -3τ ² +1, α ₁ (τ)=τ ³ -τ ² +τ, β ₀ (τ)=-2τ ³ +3τ ² , β ₁ (τ)=τ ³ -τ ² , τ∈[0, 1];

进一步，对误差进行二次型建模得到无人机运动学误差模型

Finally, the error of constructing the UAV kinematics in the segment t∈[t _i , t _i+1 ] is

Further, quadratic modeling of the error is carried out to obtain the kinematic error model of the UAV

S3: The problem of solving the UAV kinematic error model is equivalently transformed into the problem of solving linear equations. Specifically:

代入Hermit三次样条插值方程，进一步，得到分段误差二次型

其中，y_i＝[x(t_i)，x′(t_i)，x(t_i+1)，x′(t_i+1)]^T，

a_i＝α′₀E-α₀A，b_i＝α′₁E-α₁A，c_i＝β′₀E-β₀A，d_i＝β′₁E-β₁A，E为5×5维的单位矩阵；S301: For each segment

Substitute into the Hermit cubic spline interpolation equation, and further, obtain the quadratic form of piecewise error

where y _i =[x(t _i ), x'(t _i ), x(t _i+1 ), x'(t _i+1 )] ^T ,

a _i =α′ ₀ E-α ₀ A, b _i =α′ ₁ E-α ₁ A, c _i =β′ ₀ E-β ₀ A, d _i =β′ ₁ E-β ₁ A, E are 5×5 dimensional identity matrix;

恒大于0，且当控制变量确定时为一个常数，因此从误差二次型中删除该项；S302: Due to

is always greater than 0, and is a constant when the control variable is determined, so this item is deleted from the error quadratic;

S303: Convert the UAV kinematic error model to obj=min(y ^T Fy-2By), where F is a 110×110-dimensional corresponding superposition matrix of F _i , and B is a 110-dimensional vector superimposed by B _i correspondingly, y=[x(t ₀ ), x'(t ₀ ), x(t ₁ ), x'(t ₁ ), ..., x(t _f ), x'(t _f )] ^T is 110 dimensions y _i superposition;

S304: F is full rank and is a band matrix, there is a unique solution to obj=min(y ^T Fy-2By), and the solution is Fy=B.

S4: Set multiple different UAV path targets according to environmental constraints. Specifically:

According to the environmental constraints, import all the data of the initial conditions x(0) and x'(0) and some known environmental data in x(5) into y=[x(0), x'(0), x( 1), x'(1), ..., x(10), x'(10)] ^T .

S5: Bring the UAV path target as a boundary condition into the UAV's linear equation, set the control function type, and use the deep learning method to perform matrix decomposition to solve the control function parameters. Specifically:

S501: According to the requirement, set the undetermined control function u(t) with parameters as a piecewise function with 10 segments, wherein, the ith segment is u(t)=B _long ·[a _i t ² +b _i t+c _i , d _i t ² +e _i t+fi ] ^T , a _i , _bi , c _i , d _i , e _i , and _{f i are} parameters to be determined.

求解

得到

(2)判断

对应元素距离初始条件x(0)和x′(0)的全部数据以及x(5)中的部分已知环境数据是否都符合设定的误差范围要求，如果符合则停止训练，输出控制函数，如果不符合，则继续训练直到符合为止。S502: Use a neural network to solve Fy=B, and train the parameters of the control function u(t); specifically: (1) Substitute randomly selected points within the interval as parameters of the control function into B to obtain

solve

get

(2) Judgment

Whether all the data of the corresponding element distance from the initial conditions x(0) and x'(0) and some known environmental data in x(5) meet the set error range requirements, if so, stop training, output the control function, If not, continue training until it does.

S6: Judging whether the elevator declination angle calculated by the solved control parameters satisfies the UAV's own constraint condition that the elevator declination angle is not greater than 30°, if so, execute the control flight; if not, delete this type of solution and restart Execute step S5 to perform calculation until the UAV's own constraints are met, and then the flight is executed, or the preset calculation time upper limit is reached, and a no-solution warning is output.

Example 2: Similarly, taking a UAV described in the paper "Analysis and Research on Mathematical Model of UAV Based on Matlab" published by Rong Hui as an example, it is now necessary to control the UAV to execute t∈[0,10] Longitudinal flight within seconds, initially, all state variables are 0, and it is planned to use u(t)=B _long ·[t ² +2t, 2t] ^T as the control vector, it is necessary to predict all the UAV in the flight process. state. The present invention provides "a high-precision UAV real-time path planning method", which includes the following steps:

S1: Establish the linear differential equation of UAV kinematics, and obtain the UAV's own constraints and environmental constraints;

S2: Use the interpolation method to establish the kinematic error model of the UAV;

S3: Convert the solving problem of the UAV kinematic error model into a linear equation solving problem equivalently;

S4: Substitute the initial conditions and control vector into the linear equation to solve, and obtain all the states of the UAV during the flight process.

Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should Various changes may be made in details without departing from the scope of the invention as defined by the claims.

Claims (8)

1. A high-precision unmanned aerial vehicle real-time path planning method is characterized by comprising the following steps:

s1: establishing a linear state differential equation of the unmanned aerial vehicle based on a small disturbance linearization principle, and acquiring self constraint conditions and environment constraint conditions of the unmanned aerial vehicle;

s2: establishing an unmanned aerial vehicle kinematic error model by using an interpolation method;

s3: equivalently converting the problem solved by the unmanned aerial vehicle kinematic error model into a linear equation problem solved;

s4: setting a plurality of different unmanned aerial vehicle path targets according to environmental constraint conditions;

s5: taking the unmanned plane path target as a boundary condition to be brought into a linear equation of the unmanned plane, setting a control function type, and solving control function parameters by matrix decomposition by using a deep learning method;

s6: judging whether the solved control parameters meet the self constraint conditions of the unmanned aerial vehicle or not, and if so, executing control flight; if not, deleting the solution, repeating the steps S5-S6 until no solution is met, correcting the unmanned aerial vehicle path target, repeating the steps S5-S6, and if no solution is still met and the upper limit of the calculation time is reached, performing path non-solution early warning.

2. The method according to claim 1, wherein a is an nxn dimensional unmanned plane state matrix determined according to a dynamical model of the unmanned plane; u (t) is an n-dimensional control vector with respect to time; and x (t) is the state vector of the n-dimensional unmanned aerial vehicle.

3. The real-time path planning method for the high-precision unmanned aerial vehicle as claimed in claim 1, wherein the interpolation method in step S2 is Hermit cubic spline interpolation method, and t e [ t ] is an arbitrary time interval _i ，t _i+1 ]Go up throughThe interpolation method can obtain a symbolic expression of an approximate solution of the linear state differential equation in step S1 in any dimension

Wherein h is _i ＝t _i+1 -t _i ，τ＝(t-t _i )/h _i ，α ₀ (τ)＝2τ ³ -3τ ² +1，α ₁ (τ)＝τ ³ -τ ² +τ，β ₀ (τ)＝-2τ ³ +3τ ² ，β ₁ (τ)＝τ ³ -τ ² ，τ∈[0，1]。

4. The real-time path planning method for the high-precision unmanned aerial vehicle as claimed in claim 3, wherein the interval of the Hermit cubic spline interpolation method is an interval with an equal duration so as to greatly reduce the calculation amount, and the specific number i of the division sections can be adjusted according to actual precision requirements.

5. The method according to claim 1, wherein the kinematics of the UAV of step S2 is at te [ t ∈ [ t ] _i ，t _i+1 ]Error of the segment is

Further, quadratic modeling is carried out on the errors to obtain a kinematic error model of the unmanned aerial vehicle

6. The method for planning the real-time path of the high-precision unmanned aerial vehicle according to claim 1, wherein the step S3 specifically comprises:

s301: for each segment

Substituted Hermit cubic spline interpolationValue equation, and further, obtaining quadratic form of segment error

Wherein, y _i ＝[x(t _i )，x′(t _i )，x(t _i+1 )，x′(t _i+1 )] ^T ，

b _i ＝α ₁ ′E-α ₁ h _i A，

d _i ＝β ₁ ′E-β ₁ h _i A；

S302: due to the fact that

Is constantly greater than 0 and is a constant when the control variable is determined, thus removing the term from the error quadratic;

s303: unmanned aerial vehicle kinematic error model is converted into obj = min (y) ^T Fy-2 By), wherein F is F _i Is a corresponding superposition of B _i Corresponding superposition of (c), y = [ x (t) ₀ )，x′(t ₀ )，x(t ₁ )，x′(t ₁ )，…，x(t _f )，x′(t _f )] ^T Is y _i Superposition of (2);

s304: when the rank is full, obj = min (y) ^T Fy-2 By) there is a unique solution, and the solution is Fy = B.

7. The real-time path planning method for the high-precision unmanned aerial vehicle according to claim 1, wherein the step S4 is specifically as follows: planning a path by a geometric method according to environmental constraint conditions, and setting a path y = [ x (t) ₀ )，x′(t ₀ )，x(t ₁ )，x′(t ₁ )，…，x(t _f )，x′(t _f )] ^T A plurality of different drone path target values, i.e. part of the parameters in y, are known.

8. The method for planning the real-time path of the high-precision unmanned aerial vehicle according to claim 1, wherein the step S5 specifically comprises:

s501: setting the type of a parameter-containing undetermined control function u (t) according to the requirement;

s502: solving Fy = B by using deep learning, and training parameters of a control function u (t); the method comprises the following specific steps: (1) Substituting the random selected point in the interval range as the parameter of the control function into B to obtain

Solving for

To obtain

(2) Judgment of

And if the error range requirements of the set multiple different unmanned aerial vehicle path targets are met, stopping training, outputting a control function, and if the error range requirements are not met, continuing training until the error range requirements are met.

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